Commutative algebra
In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. It is foundational both for algebraic geometry and for algebraic number theory.Related pages include:
- integral domain
- quotient field
- principal ideal domain
- unique factorization domain
- Dedekind domain
- integral closure
- Chinese remainder theorem
- local ring
- Noetherian ring
- Hilbert's basis theorem
- Spectrum of a ring.
The subject's real founder, in the days when it was called ideal theory, should be considered to be David Hilbert. He seems to have thought of it (around 1900) as an alternate approach that could replace the then-fashionable complex function theory. In line with his thinking, computational aspects were secondary to the structural. The additional module concept, present in some form in Kronecker's work, is technically an improvement on working always directly on the special case of ideals. Its adoption is attributed to Emmy Noether's influence.
Given the scheme concept, commutative algebra is reasonably thought of as either the local theory or the affine theory of algebraic geometry.
"Dear hands! dear lips! I touch you and rejoice."
Were her faint tones that thrilled upon my ear.
I fell upon my knees beside her bed;
While to the aching numbness of my grief,
The tortured soul.html">soul.html">soul's most merciful relief.
For one sad.html">sad, sacred moment. Then she said,
"Maurine, my own! give not away to pain;
My soul may hear the summons and pass on.
And when refreshed, come hither. I grow weak
And make my dying.html">dying wishes known to-night.html">night.
Which seemed to fill the room.html">room with golden light,
Of coming night, I entered that dim room,
And on the pillow at her side.html">side there smiled
My heart has dwelt in an enchanted land;
Without one drop of anguish or alloy.
Or sad-eyed Sorrow fills it full of tears,
Who linger long upon this troubled way,
To mingle with His angels, who alone
I do not murmur. God has heaped my measure,
And, from the fulness of an earthly love.html">love,
Before I even brush the skirts of Woe.
"I leave my aged parents here below,
Be kind to them, and love them to the end,
A soul immortal in your charge, Maurine.
Till God shall claim her, she is yours to keep,
She touched the slumb'ring cherub at her side,
And laid the precious burden on my breast.
A solemn silence fell upon the scene.
My yielding bosom with her waxen cheek,
Such wordless joy possessed me.
Oh! at last
Had caused my soul such travail, was my own:
mine.html">Mine own to cherish--wholly mine alone.
Was now restored, and given back to me.
The dying voice continued:
You yet have me, whose mortal life she cost.
And good within me, lives in her again.
.
On
wordlookup.net
All is still licensed under the GNU FDL.
It uses material from the wikipedia.
|
|